Weak universality for a class of 3d stochastic reaction-diffusion models

Marco Furlan and Massimiliano Gubinelli

First issued 10 August 2017 · PDF · HTML

Abstract

We establish the large scale convergence of a class of stochastic weakly nonlinear reaction-diffusion models on a three dimensional periodic domain to the dynamic $\Phi^4_3$ model within the framework of paracontrolled distributions. Our work extends previous results of Hairer and Xu to nonlinearities with a finite amount of smoothness (in particular $C^9$ is enough). We use the Malliavin calculus to perform a partial chaos expansion of the stochastic terms and control their $L^p$ norms in terms of the graphs of the standard $\Phi^4_3$ stochastic terms.

Versions

1. Version 3 (arXiv v2) current
   26 January 2018
   arXiv comments: 51 pages, exposition substantially improved
   PDF · TeXmacs source · files and digests · arXiv:1708.03118
2. Version 2 (arXiv v1)
   10 August 2017
   arXiv comments: 45 pages
   PDF · LaTeX source · files and digests · arXiv:1708.03118
3. Version 1
   written 9 August 2017, not public at the time
   PDF · TeXmacs source · files and digests

Cite

Marco Furlan and Massimiliano Gubinelli. Weak universality for a class of 3d stochastic reaction-diffusion models. Papers of Massimiliano Gubinelli, 2017, version 3. https://mgubi.org/papers/paper/phi43-weak-universality/

Licence: Creative Commons Zero v1.0 Universal

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